Oscillator device, optical deflector and image forming apparatus using the optical deflector

ABSTRACT

An oscillator device includes an oscillation system having first and second oscillators and first and second resilient supporting members, wherein the oscillation system has at least two frequencies of natural oscillation mode around a torsion axis which include a first resonance frequency f 1  and a second resonance frequency f 2 , wherein there is a relationship that f 2  is approximately two-fold of f 1 , and wherein a drive control member supplies, to a driving member, a driving signal which is comprised of a driving signal based on synthesizing a first driving signal having a first driving frequency and a second driving signal having a second driving frequency, and which is such driving signal that, among the first and second driving frequencies, a lower-frequency side driving frequency Df 1  and a higher-frequency side driving frequency Df 2  satisfy a relationship 
     
       
      
       Df 
       1×2= 
       Df 
       2  
      
     
     and that Df 2  satisfies a relationship 
     
       
      
       f 
       2−| 
       Δf/ 
       2|&lt; 
       Df 
       2&lt; 
       f 
       2+|Δ 
       f/ 
       2|.

TECHNICAL FIELD

This invention relates to an oscillator device having a plurality of oscillators and, more particularly, to an oscillator device which is suitably applicable to an optical deflector. In another aspect, the invention concerns a scanning display unit or an mage forming apparatus such as a laser beam printer or a digital copying machine, for example, having such optical deflector.

BACKGROUND ART

A large variety of optical deflectors having a resonance-oscillated mirror have been proposed. The resonance type optical deflector has the following features, as compared with a conventional optical-scanning optical system using a rotary polygonal mirror such as a polygon mirror: that is, the size of the device can be made very small and the power consumption can be kept low. Particularly, an optical deflector comprising Si monocrystal, which is produced through the semiconductor process, has theoretically no metal fatigue and thus the durability thereof is very good.

On the other hand, in the resonance type deflector, since the displacement angle of the mirror changes theoretically sinusoidally, the angular speed of deflected light is not constant. The following techniques have been proposed to correct this characteristic (see U.S. Pat. No. 4,859,846, U.S. Pat. No. 5,047,630 and U.S. Pat. No. 7,271,943).

In U.S. Pat. No. 4,859,846 and U.S. Pat. No. 7,271,943, a resonance type deflector having an oscillation mode based on a fundamental frequency and a frequency three-fold the fundamental frequency, is used to achieve the driving in which the displacement angle of the mirror changes like a chopping wave.

FIG. 13 shows a micromirror which realizes such chopping-wave drive. In FIG. 13, an optical deflector 12 is comprised of oscillators 14 and 16, resilient supporting members 18 and 20, driving members 23 and 50, detecting elements 15 and 32, and a control circuit 30. This micromirror has a fundamental resonance frequency and a resonance frequency approximately three-fold the fundamental frequency, and it is driven at a combined frequency of the fundamental frequency and the three-fold frequency. Based on this, the oscillator 14 having a mirror surface is driven by a chopping-wave drive, such that optical deflection with a smaller angular speed change in the displacement angle is accomplished as compared with the sinusoidal drive.

During the driving, the oscillation of the oscillator 14 is detected by the detecting elements 15 and 32, and a driving signal necessary for the chopping wave is generated by the control circuit 30. The driving signal is inputted to the driving members 23 and 50, by which the micromirror is driven. As described above, since the angular speed of the scanning deflection has an approximately-constant angular-speed region which is widened as compared with a case where the displacement angle is based on a sinusoidal wave, the available region relative to the whole area of scanning deflection is enlarged. Here, the drive is performed in accordance with the fundamental frequency and a frequency three-fold the fundamental frequency or, alternatively, a driving frequency based on a three-fold frequency and a one-third frequency of that.

DISCLOSURE OF THE INVENTION

Although chopping wave driving or sawtooth-wave driving of the oscillator of the oscillator device (optical deflector) can be realized by the proposals made in the aforementioned patent documents, further improvements are necessary in regard to the controllability of the displacement angle of the oscillator. Thus, the present invention provides an oscillator device suitable for precise control of the displacement angle.

In accordance with an aspect of the present invention, there is provided an oscillator device, comprising: an oscillation system including a first oscillator, a second oscillator, a first resilient supporting member configured to support said first oscillator for torsional oscillation about a torsion axis relative to said second oscillator, and a second resilient supporting member configured to support said second oscillator for torsional oscillation about a torsion axis relative to a fixed member; driving means configured to drive said oscillation system; and drive control means configured to supply a driving signal to said driving means; wherein said oscillation system has at least two frequencies of natural oscillation mode around the torsion axis which include a first resonance frequency f1 and a second resonance frequency f2, wherein there is a relationship that f2 is approximately two-fold of f1, and wherein said drive control means supplies, to said driving means, a driving signal which is comprised of a driving signal based on synthesizing a first driving signal having a first driving frequency and a second driving signal having a second driving frequency, and which is such driving signal that, among the first and second driving frequencies, a lower-frequency side driving frequency Df1 and a higher-frequency side driving frequency Df2 satisfy a relationship

Df1×2=Df2

and that Df2 satisfies a relationship

f2=|Δf/2|<Df2<f2+|Δf/2|.

In the oscillation system, Δf which is expressed by Δf=f2−2×f1 may satisfy a relationship Δf<0.

When a displacement angle of said oscillator is denoted by θ, an amplitude of a first vibrating motion is denoted by A₁, an angular frequency of the first vibrating motion is denoted by •₁, an amplitude of a second vibrating motion is denoted by A₂, an angular frequency of the second vibrating motion is denoted by ω₂ (ω₂=2×ω₁), a relative phase difference of the two frequencies is denoted by φ, and time is denoted by t, said drive control means may supply to said driving means a driving signal effective to cause at least one of said first and second oscillators to produce oscillation which is represented by an expression:

θ(t)=A ₁ sin ω₁ t+A ₂ sin (ω₂ t+φ).

When B₁ denotes an amplitude component of a lower-frequency side driving signal, B₂ denotes an amplitude component of a higher-frequency side driving signal, ω₁ denotes an angular frequency of the lower-frequency side driving signal, ω₂ denotes an angular frequency of the higher-frequency side driving signal (ω₂=2×ω₁), ψ denotes a relative phase difference, and t denotes time, the driving signal may be represented by an expression:

P=B ₁ sin ω₁ t+B ₂ sin (ω₂ t+ψ).

The drive control means may supply, to said driving means, a driving signal which satisfies a relation

f2−f2×2.8×10⁻⁴ <Df2<f2+f2×2.6×10⁻⁴.

The drive control means may supply, to said driving means, a driving signal which satisfies a relation

f2−f2×2.1×10⁻⁴ <Df2<f2+f2×2.1×10⁻⁴.

The drive control means may supply, to said driving means, a driving signal which satisfies a relation

f2−f2×1×10⁻⁴ <Df2<f2+f2×1×10⁻⁴.

The drive control means may further supply, to said driving means, a driving signal which satisfies relationships Df1<f1 and Df2≧f2.

In accordance with another aspect of the present invention, there is provided an optical deflector including an oscillator device as recited above, wherein said first oscillator may be provided with an optical deflection element.

In accordance with a further aspect of the present invention, there is provided an image forming apparatus, comprising: an optical deflector as recited above; an optical system; a light source; and a photosensitive member, wherein a light beam from said light source is scanningly deflected by said optical deflector, and the scan light is collected by said optical system at a target position on said photosensitive member.

With the oscillator device of the present invention, more stable driving is enabled relative to external disturbance, and jitter during the oscillation of the oscillator is reduced. Thus, high accuracy control of the displacement angle of the oscillator is enabled.

These and other objects, features and advantages of the present invention will become more apparent upon a consideration of the following description of the preferred embodiments of the present invention taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating an oscillator device according to the present invention.

FIG. 2 is a block diagram of an oscillator device according to the present invention.

FIGS. 3A and 3B are diagrams illustrating vibrational motion of an oscillator device according to the present invention, wherein FIG. 3A shows the relationship between time and the displacement angle and FIG. 3B shows the result of differentiating, with respect to time, the expression which presents the relationship between time and the displacement angle of FIG. 3A.

FIGS. 4A and 4B are diagrams of open-loop transfer characteristic when the driving frequency is determined with reference to the resonance frequency f1 of the oscillation system, wherein FIG. 4A shows the gain characteristic and FIG. 4B shows the phase characteristic.

FIGS. 5A and 55 are diagrams of open-loop transfer characteristic when the driving frequency is determined with reference to the resonance frequency f2 of the oscillation system, wherein FIG. 5A shows the gain characteristic and FIG. 5B shows the phase characteristic.

FIG. 6 is a diagram which illustrates the relationship between an error, [%] of the driving frequency Df2 and the resonance frequency f2 of the oscillation system, and the scan jitter.

FIGS. 7A and 7B are diagrams illustrating the transfer characteristic when Δf=+6, wherein FIG. 7A shows the gain characteristic and FIG. 7B shows the phase characteristic.

FIGS. 8A and 8B are diagrams illustrating the transfer characteristic when Δf=−6, wherein FIG. 8A shows the gain characteristic and FIG. 8B shows the phase characteristic.

FIG. 9 is a diagram showing the resonance characteristic (the relationship between the driving frequency and the amplitude) around the first resonance frequency f1.

FIG. 10 is a diagram showing the resonance characteristic (the relationship between the driving frequency and the amplitude) around the second resonance frequency f2.

FIG. 11 is a diagram illustrating an example of the relationship between the resonance frequencies f1 and f2 and the driving frequencies Df1 and Df2 of the oscillation system.

FIG. 12 is a diagram illustrating an image forming apparatus using an oscillator device according to the present invention.

FIG. 13 is a block diagram which shows the structure of a conventional optical deflecting device.

BEST MODE FOR PRACTICING THE INVENTION

Preferred embodiments of the present invention will now be described with reference to the attached drawings.

First Embodiment

A first embodiment of an oscillator device according to the present invention will be explained. The oscillation system 100 of the present embodiment comprises a first oscillator 101 and a second oscillator 102 as shown in FIG. 1. Furthermore, it comprises a first resilient supporting member 111 for supporting the first oscillator 101 for torsional oscillation about a torsion axis relative to the second oscillator 102, and a second resilient supporting member 112 for supporting the second oscillator 102 for torsional oscillation about a torsion axis relative to a fixed member 121.

An optical deflection element such as a reflection member may be formed on the surface of the first oscillator 101, for example and, in that occasion, the oscillator device can be used as an optical deflector. The reflection member may be provided by forming a metal thin film such as aluminum by sputtering, for example.

Furthermore, the oscillation system of the present embodiment may have a structure other than the cantilevered structure shown in FIG. 1: e.g., an oscillation system having a structure supported at opposite ends or an oscillation system having a combined structure of cantilevered structure and opposite-end-supported structure, as proposed by Japan Patent No. 4027359.

Driving means 120 has a structure based on an electromagnetic system, an electrostatic system or a piezoelectric system, for example, to apply a driving force to the oscillation system 100. In the case of electromagnetic driving, as an example, a permanent magnet may be provided on at least one oscillator, and an electric coil for applying a magnetic field to this permanent magnet may be disposed adjacent the oscillator. The disposition of the permanent magnet and the electric coil may be reversed. In the case of electrostatic driving, an electrode may be formed on at least one oscillator, and an electrode for providing an electrostatic force acting between it and this electrode may be formed adjacent the oscillator. In the case of piezoelectric driving, a piezoelectric element may be provided in the oscillation system or on the supporting member to apply a driving force.

The oscillation system 100 has at least two natural-oscillation-mode frequencies around the torsion axis, that is, a first resonance frequency f1 and a second resonance frequency f2.

There is a relationship that f2 is approximately two-fold of f1. Here, the approximately two-fold relationship means that f1 and f2 are in the relationship of 1.98≦f2/f1≦2.02. The reason that the frequency f2 may not be exactly twice the frequency f1 is that there may be a processing error in the manufacture of the oscillation system.

The displacement angle θ of the oscillator device of the present embodiment is such as follows. When the amplitude, angular frequency and phase of the first vibrating motion are denoted by A₁, ω₁ and φ₁, respectively, and the amplitude, angular frequency and phase of the second vibrating motion are denoted by A₂, ω₂ and φ₂, respectively, and when time where an appropriate time is taken as an origin or reference time is denoted by t, the displacement angle can be expressed as follows.

θ(t)=A ₁ sin (ω₁ t+φ ₁)+A ₂ sin (ω₂ t+φ ₂)  (1)

Furthermore, when the amplitude of the first vibrating motion is denoted by A₁ and the angular frequency thereof is denoted by ω₁ and the amplitude of the second vibrating motion is denoted by A2 and the angular frequency thereof is denoted by ω₂, and a relative phase difference between the frequency of the first vibrating motion and the frequency of the second vibrating motion is denoted by and time is denoted by t, the displacement angle θ of the oscillator device can be expressed as follows.

θ(t)=A ₁ sin ω₁ t+A ₂ sin (ω₂ t+φ)  (2)

The vibrating motion of such oscillation system 100 is illustrated in FIG. 3A. Namely, the oscillation system produces a vibrating motion which is the composite of a vibrating motion represented by θ(t)=A₁ sin (ω₁t) and a vibrating motion represented by θ(t)=A₂ sin (ω₂t+φ). Furthermore, FIG. 3B shows the results obtained by differentiating expression (1) which represents the vibrating motion of this oscillation system. As shown in FIG. 3B, the oscillation system 100 has a period in which it moves approximately at a constant angular-speed.

Drive control means 150 generates such driving signal that causes the oscillation system to produce vibrating motion represented by expression (1) or (2), the driving signal being supplied to the aforementioned driving means.

With regard to the driving signal, any signal may be may be used provided that the oscillator produces oscillation represented by expression (1) or (2). For example, it may be a driving signal based on synthesizing sinusoidal waves. Alternatively, it may be a pulse-like driving signal. In the case of a driving signal based on synthesizing sinusoidal waves, as an example, the driving signal may be one that can be represented by an expression including at least a term B₁ sin ω₁t+B₂ sin (ω₂t+ψ). Here, B₁ and B₂ are amplitude components, ψ is the relative phase difference, ω₁ and ω₂ are driving angular frequencies, and t is time. In this case, a desired driving signal can be obtained by adjusting the amplitude and phase of each sinusoidal wave. Furthermore, if the driving is made using pulse-like signals, a desired driving signal can be generated by changing the pulse number, pulse spacing, pulse width or the like, with respect to time.

Displacement angle detecting means 140 can detect the displacement angle of at least one of the first oscillator 101 and the second oscillator 102. In the case of FIG. 1, the displacement angle detecting means 140 comprises a photodetector. A light beam 132 emitted from a light source 131 is reflected by the first oscillator 101, and the reflected light 133 is detected by this photodetector 140. Actually, there are two photodetectors 140 disposed at positions leaning to the center than the maximum displacement angle of the first oscillator. In other words, the photodetectors are disposed at the positions of BD1 and BD2 in FIG. 3A. By disposing the photodetectors in the manner described above, four time moments (t10, t20, t30 and t40) can be detected within a single period. The drive control means 150 detects the state of displacement of the oscillator based on these four time moments, and it generates a driving signal for driving the oscillation system based on the detected displacement state.

It should be noted that, although in this embodiment the oscillation of the oscillator is detected using photodetectors, a piezoresistor may be provided on the resilient supporting members 111 and 112, and the displacement state of the oscillator may be detected based on the output signal of the piezoresistor.

Next, the control of the displacement angle of the oscillator device in the present embodiment will be explained.

FIG. 2 is a block diagram of the oscillator device of the present embodiment. The driving means 120 applies a driving force to the oscillation system 100. Displacement sensing means 140 detects the displacement angle of the oscillator which constitutes an oscillation system. The drive control means 150 adjusts the driving force so that the oscillator takes a desired displacement angle.

The displacement angle detecting means 140 measures four different time moments during a single period of the aforementioned first vibrating motion, that is, two different time moments (t10 and t20) where the oscillator takes a first displacement angle and two different time moments (t30 and t40) where the oscillator takes a second displacement angle. since the oscillation of the oscillation system is expressed in terms of four variables or three variables as shown in expression (1) and expression (2), these variables can be calculated from the four measured time moments.

The drive control means 150 generates a driving signal based on synthesizing a first signal having a first frequency and a second signal having a second frequency, and supplies it to the aforementioned driving means 120.

Additionally, it adjusts the driving signal so that the four measured time moments coincide with preset time moments. By supplying so adjusted driving signal to the driving means 120, the oscillator device can be controlled very precisely.

More specifically, the drive control means 150 calculates at least one of the values A₁, φ₁, A₂ and φ₂ of expression (1) which presents the displacement angle of the oscillator device, from the signal of the displacement angle detecting means 140. Then, the driving signal can be adjusted so that at least one of these values becomes equal to a preset value. Furthermore, in the case of expression (2), at least one of the values A1, A2 and φ is calculated, and the driving signal is adjusted so that at least one of these values becomes equal to a preset value. By supplying so adjusted driving signal to the driving means 120, the oscillator device can be controlled very precisely.

However, in this embodiment, based on the relationship of the higher-frequency side driving frequency Df2 of the driving signal and the second resonance frequency f2, the controllability thereof is different. Namely, when a driving signal based on synthesizing a first driving signal having a first driving frequency and a second driving signal having a second driving frequency is supplied to the driving means, by supplying a driving signal having a relationship such as follows to the driving means the controllability of the oscillator device is improved. First of all, the lower-frequency side driving frequency Df1 and the higher-frequency side driving frequency Df2 of the first and second driving frequencies are controlled to satisfy a relationship Df1×2=Df2. Furthermore, f2 which is the higher-frequency side resonance frequency of the oscillation system and Δf and Df2 which are obtainable by expression (3) below are controlled to satisfy the relationship of expression (4) below.

Δf=f2−2×f1  (3)

f2−|Δf/2|<Df2<f2+|Δf/2|  (4)

The driving frequency of the oscillator device can be determined by a method A or a method B, as follows.

[Method A]

Df1 is so determined that the resonance frequency f1 of the oscillation system and the driving frequency Df1 thereof coincide with each other or, alternatively, they become close to each other. Df2 is determined by doubling Df1. In this specification, the manner of determining the driving frequency taking f1 as a reference will be referred to as “f1 reference driving”.

[Method B]

Df2 is so determined that the resonance frequency f2 of the oscillation system and the driving frequency Df2 thereof coincide with each other or, alternatively, they become close to each other. Df1 is determined by multiplying Df2 by ½. In this specification, the manner of determining the driving frequency taking f2 as a reference will be referred to as “f2 reference driving”.

Now, the difference in the open-loop transfer characteristic with regard to φ in expression (2) which presents the displacement angle of the oscillator device will be explained.

FIGS. 4A and 45 illustrate the open-loop transfer characteristic in the case of “f1 reference driving”. FIG. 4A shows the gain characteristic, and FIG. 4B shows the phase characteristics. The values of f1, f2, Df1, Df2 and Δf in FIGS. 4A and 4B are: f1=2531 Hz, f2=5068 Hz, Df1=2531 Hz, Df2=5062 Hz, Δf=6.

Furthermore, FIGS. 5A and 5B illustrate the open-loop transfer characteristic in the case of “f2 reference driving”. FIG. 5A shows the gain characteristic, and FIG. 5B shows the phase characteristics. The values of f1, f2, Df1, Df2 and Δf in FIGS. 5A and 5B are: f1=2531 Hz, f2=5068 Hz, Df1=2534 Hz, Df2=5068 Hz, and Δf=6.

Comparing FIG. 4B with FIG. 55, it is seen that in the case of “f1 reference driving” there is a large phase delay particularly in the band of 100 Hz or more, than the case of “f2 reference driving”.

Comparing the phase at 200 Hz, for example, it is −44 deg. in the case of “f1 reference driving”; whereas it is 52 deg. in the case of “f2 reference driving” and the phase margin is larger. If the phase margin is large as mentioned above, the stability against the external disturbance improves. Furthermore, since the gain increases if the phase margin is large, the controllability band increases, reducing the jitter.

On the contrary, if the phase margin is small, the stability against the external disturbance is degraded. Furthermore, in order to enlarge the phase margin, the gain has to be lowered until a sufficient phase margin (e.g., 30 deg.) is obtained. Namely, in this case, since the gain is lowered, the controllability band decreases, causing an increase of jitter.

It is seen from the above that, with the “f2 reference driving” as compared with the “f1 reference driving”, the optical deflecting device can be controlled more precisely.

Furthermore, it has been confirmed by experiments that, in the case of “f2 reference driving”, the scan precision of the oscillator device changes depending on the rate of deviation of the higher-frequency side driving frequency Df2 of the driving signal from the resonance frequency f2 of the oscillation system. FIG. 6 illustrates the relationship of the error [%] between the driving frequency Df2 and the resonance frequency f2 of the oscillation system with the scan jitter. The values of f1, f2, Df1, Df2 and Δf in FIG. 6 are: f1=2531 Hz, f2=5068 Hz, Df1=2531 Hz, Df2=5062 Hz and Δf=6. The term “scan jitter” refers to the variation of time in which the scan center is passed through, taking the 80% position of the largest scan amplitude of the oscillator device as a reference. The scan jitter ratio is 1 when Df2=f2. In this embodiment, the position corresponding to 80% of the largest scan amplitude is taken as the reference, and the observation point is set at the scan center. However, this reference may be based on other position in the scan region.

It is seen from FIG. 6 that the scan jitter ratio is minimum when the error [%] between the driving frequency Df2 and f2 is zero. Also, it is seen from FIG. 6 that, in order to hold the scan jitter at 50% or less, the scan jitter ratio has to be kept at 1.5 or lower. Here, the driving frequency Df2 of the driving signal P should be such as shown in expression (5) below.

f2−f2×2.8×10⁻⁴ <Df2<f2+f2×2.6×10⁻⁴  (5)

In this case, since the adjustment accuracy of the driving frequency Df2 is widened, the circuitry of the driving member can be simplified and the precision for detecting the second resonance frequency f2 can be made lower. Therefore, the circuitry cost can be reduced while suppressing the scan jitter to some extent.

Furthermore, in order to hold the scan jitter at 10% or less, the scan jitter ratio has to be kept at 1.1 or lower. Here, the driving frequency Df2 of the driving signal P should be such as shown in expression (6) below.

f2−f2×1×10⁻⁴ <Df2<f2+f2×1×10⁻⁴  (6)

In this case, individual difference of the scan jitter of the oscillator device can be reduced, and also high precision control of the displacement angle is enabled.

Furthermore, in order to hold the scan jitter at 30% or less, the scan jitter ratio has to be kept at 1.3 or lower. Here, the driving frequency Df2 of the driving signal P should be such as shown in expression (7) below.

f2−f2×2.1×10⁻⁴ <Df2<f2+f2×2.1×10⁻⁴  (7)

In this case, both of the reduction of the circuitry cost and the controllability of the displacement angle can be accomplished at the same time.

Second Embodiment

Next, a second embodiment of an oscillator device according to the present invention will be described. The oscillator device according to the second embodiment has basically the same structure and driving method as those of the first embodiment. Using an oscillation system that satisfies the condition mentioned below in the oscillator device of the second embodiment, the control characteristic is improved furthermore. Namely, the oscillation system is such that the value Δf of expression (3) satisfies the following conditional expression.

Δf<0  (8)

Here, in order to illustrate that the control characteristic improves in an oscillator device having an oscillation system satisfying the condition of expression (8), the difference of the open-loop transfer characteristic of A₁ which is one of the control parameters of expressions (1) and (2) presenting the displacement angle of the oscillator of the oscillator device will be explained.

FIGS. 7A and 78 are diagrams illustrating the open-loop transfer characteristic in a case where f1=2531 Hz, f2=5068 Hz, Df1=2534 Hz, Df2=5068 Hz and Δf=+6 Hz. FIG. 7A shows the gain characteristic and FIG. 7B shows the phase characteristic.

Furthermore, FIGS. 8A and 8B are diagrams illustrating the open-loop transfer characteristic in a case where f1=2523 Hz, f2=5040 Hz, Df1=2520 Hz, Df2=5040 Hz and Δf=−6 Hz. FIG. 8A shows the gain characteristic and FIG. 8B shows the phase characteristic.

Comparing FIG. 7B and FIG. 8B, it is seen that, in the case where Δf is +6 Hz as compared with the case where Δf is −6 Hz, there is a large phase delay particularly in the band of 100 Hz or higher.

For example, comparing the phase at 260 Hz where the gain becomes equal to zero, it is seen that, although it is only 18 deg. in the case of Δf=+6 Hz, it is as large as 55 deg. in the case of Δf=−6 Hz and thus the phase margin is quite large.

If the phase margin is large as described, the stability against external disturbance is improved. Furthermore, since the gain can be increased if the phase margin is large, the control band goes up which in turn leads to a reduction of the jitter.

If, to the contrary, the phase margin is small, the stability against external disturbance is degraded. Furthermore, in order to enlarge the phase margin, the gain has to be lowered until a sufficient phase margin (e.g., 30 deg.) is obtained. Namely, since in this case the gain is lowered, the control band goes down which in turn causes an increase of the jitter.

It is seen from the above that the phase margin can be made larger in the oscillation system of Δf=−6 Hz as compared with the oscillation system of Δf=+6 Hz and that, as a result of this, the jitter can be reduced more and the oscillator device can be controlled more precisely. Hence, when the oscillation system of the oscillator device of the present embodiment is made to satisfy the relationship of expression (8) mentioned above, the control characteristic of the oscillator device is improved.

FIG. 9 illustrates the resonance characteristic (the relationship between the driving frequency and the amplitude) around the first resonance frequency f1. It is seen from FIG. 9 that, if the driving frequency deviates from the position of the resonance point where the amplitude value of the oscillator becomes largest, the amplitude value of the oscillator decreases. In other words, the driving efficiency of the oscillator device is slowed down. Although in the condition mentioned above the range of Δf is limited solely to the minus side, since the driving efficiency is slowed down if the driving frequency largely deviates from the resonance frequency, it results in an increase of the power consumption or generation of heat, for example. Therefore, in this case, the driving efficiency at the first resonance frequency should be taken into account and the range of Δf should be limited to the range of expression (9). Then, the oscillator device can be driven more efficiently.

−2×(f1b−f1a)≦Δf<0  (9)

Here, f1 a denotes the frequency with which, at the lower-frequency side of the resonance peak of the first resonance frequency f1, the vibrational energy becomes equal to the mesial magnitude of the resonance peak, and f1 b denotes the frequency with which, at the higher-frequency side of the resonance peak, the vibrational energy becomes equal to the mesial magnitude of the resonance peak.

FIG. 10 illustrates the resonance characteristic (the relationship between the driving frequency and the amplitude) around the second resonance frequency f2. It is seen from FIG. 10 that, if the driving frequency deviates from the position of the resonance point where the amplitude value of the oscillator becomes largest, the amplitude value of the oscillator decreases. In other words, the driving efficiency of the oscillator device is slowed down. Although in the condition mentioned above the range of Δf is limited solely to the minus side, since the driving efficiency is slowed down if the driving frequency largely deviates from the resonance frequency, it results in an increase of the power consumption or generation of heat, for example. Therefore, in this case, the driving efficiency at the first resonance frequency should be taken into account and the range of Δf should be limited to the range of expression (10). Then, the oscillator device can be driven more efficiently.

(f1d−f1c)≦Δf<0  (10)

Here, f1 c denotes the frequency with which, at the lower-frequency side of the resonance peak of the second resonance frequency f2, the vibrational energy becomes equal to the mesial magnitude of the resonance peak, and f1 d denotes the frequency with which, at the higher-frequency side of the resonance peak, the vibrational energy becomes equal to the mesial magnitude of the resonance peak.

On the other hand, during the manufacturing process of the oscillation system of the oscillator device, an error occurs in the spring constant of the resilient supporting member or in the inertia moment of the oscillator when the oscillation system is made. This means that an error occurs in the resonance frequency of the oscillation system which is determined by the spring constant of the resilient supporting member and the inertia moment of the oscillator. In such case, an error of Δf resulting from the error of the resonance frequency may be predicted beforehand and, from this error amount, the range for Δf may be determined. Here, the error of Δf may be detect theoretically by calculating the error amount of the spring constant or the inertia moment or, alternatively, it may be detected statistically from errors of Δf of manufactured devices. By limiting the range of Δf as shown in expression (11) based on the predicted error amount of Δf, regardless of manufacture dispersions the oscillator can be made within the range of Δf<0.

(Δfu−Δf1)≦Δf<0  (11)

Here, Δf1 denotes the lower-limit side minimum value within the dispersion range of Δf, and Δfu denotes the upper-limit side maximum value.

Furthermore, if the driving is made so that, among the two driving frequencies of the driving signal, the lower-frequency side driving frequency Df1 and the higher-frequency side driving frequency Df2 satisfy the conditions of expression (12), expression (13) and expression (14), the control characteristic is improved more.

Df1<f1  (12)

Df2≧f2  (13)

Df1×2=Df2  (14)

FIG. 11 is a diagram exemplifying the relationship between the resonance frequencies f1 and f2 of the oscillation system of the present embodiment and the driving frequencies Df1 and Df2. If the conditions of expression (3) and expression (8) are satisfied and, in addition, the conditions of expression (12), expression (13) and expression (14) are satisfied, the two resonance frequencies f1 and f2 are present between the driving frequencies Df1 and Df2 as shown in FIG. 11. Particularly, in this embodiment, by driving the oscillator device at Df2=f2 or, alternatively, to cause Df2 to come close to f2 as much as possible, the oscillator device can be drive-controlled more precisely.

Third Embodiment

Referring to FIG. 12, an embodiment in which an oscillator device according to the present invention is applied to an image forming apparatus will be explained.

An optical deflecting device 500 to be used in an image forming apparatus of the present embodiment corresponds to an oscillator device described with reference to the first embodiment. A light beam emitted from a light source 510 is shaped by a collimator lens 520 which is an optical system and, after this, it is deflected one-dimensionally by the optical deflecting device 500. The thus deflected scanning light is collected by a coupling lens 530 which is an optical system toward a target position on a photosensitive member 540. By this, an electrostatic latent image is formed on the photosensitive member 540. There are two photodetectors 550 disposed at the scan ends of the optical deflecting device. The optical deflecting device 500 detects the vibrational state of the oscillator in the manner having been described with reference to the first embodiment, and a driving signal is determined.

In the image forming apparatus of the present embodiment, by driving the oscillator device under the conditions explained in the first embodiment, an image forming apparatus of better control characteristic and higher precision can be accomplished.

While the invention has been described with reference to the structures disclosed herein, it is not confined to the details set forth and this application is intended to cover such modifications or changes as may come within the purposes of the improvements or the scope of the following claims. 

1. An oscillator device, comprising: an oscillation system including a first oscillator, a second oscillator, a first resilient supporting member configured to support said first oscillator for torsional oscillation about a torsion axis relative to said second oscillator, and a second resilient supporting member configured to support said second oscillator for torsional oscillation about a torsion axis relative to a fixed member; driving means configured to drive said oscillation system; and drive control means configured to supply a driving signal to said driving means; wherein said oscillation system has at least two frequencies of natural oscillation mode around the torsion axis which include a first resonance frequency f1 and a second resonance frequency f2, wherein there is a relationship that f2 is approximately two-fold of f1, and wherein said drive control means supplies, to said driving means, a driving signal which is comprised of a driving signal based on synthesizing a first driving signal having a first driving frequency and a second driving signal having a second driving frequency, and which is such driving signal that, among the first and second driving frequencies, a lower-frequency side driving frequency Df1 and a higher-frequency side driving frequency Df2 satisfy a relationship Df1×2=Df2 and that Df2 satisfies a relationship f2−|Δf/2|<Df2<f2+|Δf/2|.
 2. An oscillator device as claimed in claim 1, wherein, in said oscillation system, Δf which is expressed by Δf=f2−2×f1 satisfies a relationship Δf<0.
 3. An Oscillator device as claimed in claim 1, wherein, when a displacement angle of said oscillator is denoted by θ, an amplitude of a first vibrating motion is denoted by A₁, an angular frequency of the first vibrating motion is denoted by ω₁, an amplitude of a second vibrating motion is denoted by A₂, an angular frequency of the second vibrating motion is denoted by ω₂ (ω₂=2×ω₁), a relative phase difference of the two frequencies is denoted by φ, and time is denoted by t, said drive control means supplies to said driving means a driving signal effective to cause at least one of said first and second oscillators to produce oscillation which is represented by an expression: θ(t)=A ₁ sin ω₁ t+A ₂ sin (ω₂ t+φ).
 4. An oscillator device as claimed in claim 1, wherein, when B₁ denotes an amplitude component of a lower-frequency side driving signal, B₂ denotes an amplitude component of a higher-frequency side driving signal, ω₁ denotes an angular frequency of the lower-frequency side driving signal, ω₂ denotes an angular frequency of the higher-frequency side driving signal (ω₂=2×ω₁), ψ denotes a relative phase difference, and t denotes time, the driving signal is represented by an expression: P=B ₁ sin ω₁ t+B ₂ sin (ω₂ t+ψ).
 5. An oscillator device as claimed in claim 1, wherein said drive control means supplies, to said driving means, a driving signal which satisfies a relation f2−f2×2.8×10⁻⁴ <Df2<f2+f2×2.6×10⁻⁴.
 6. An oscillator device as claimed in claim 1, wherein said drive control means supplies, to said driving means, a driving signal which satisfies a relation f2−f2×2.1×10⁻⁴ <Df2<f2+f2×2.1×10⁻⁴.
 7. An oscillator device as claimed in claim 1, wherein said drive control means supplies, to said driving means, a driving signal which satisfies a relation f2−f2×1×10⁻⁴ <Df2<f2+f2×1×10⁻⁴.
 8. An oscillator device as claimed in claim 2, wherein said drive control means further supplies, to said driving means, a driving signal which satisfies relationships Df1<f1 and Df2≧f2.
 9. An optical deflector including an oscillator device as claimed in claim 1, wherein said first oscillator is provided with an optical deflection element.
 10. An image forming apparatus, comprising: an optical deflector as claimed in claim 9; an optical system; a light source; and a photosensitive member, wherein a light beam from said light source is scanningly deflected by said optical deflector, and the scan light is collected by said optical system at a target position on said photosensitive member. 